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10.02 - Vapor-Liquid Equilibrium (VLE) Calculations Click here. 44 5

Use VLookup and Eqn. 2.47 to tabulate shortcut estimates of Antoine coefficients. (6min, uakron.edu) By calculating these in a distinct location, then referencing those estimates in the cells that will actually be used for later calculations, you can type in precise estimates when you have them. When no precise values are available, recover the shortcut estimates by simply typing "=" and referencing the cell with the shortcut estimate. This screencast includes sample calculations of the shortcut Antoine coefficients of methanol and benzene.

Comprehension Questions:

1. Estimate the Antoine "A" coefficient for methanol according to the shortcut method.
2. Estimate the Antoine "B" coefficient for benzene according to the shortcut method.
3. Estimate the Antoine "C" coefficient for ethanol according to the shortcut method. Compare to the "C" coefficient reported in Apx. E.
4. Estimate the Antoine "A" coefficient for ethanol according to the shortcut method. Compare to the "A" coefficient reported in Apx. E.
5. Estimate the Antoine "B" coefficient for water according to the shortcut method. Compare to the "A" coefficient reported in Apx. E.
11.12 - Lewis-Randall Rule and Henry's Law Click here. 44 5

Henry's Law can be used to compute VLE of gases in solvents. We can estimate Henry's "constants" (uakron.edu, 12min) by Eqns. 11.64 and 11.68. Here we demonstrate the procedure for CO2+toluene and CO2+water. In some cases, the estimates can be good and in some cases they can be quite bad. The only way to know for sure is to validate your model with experimental data. Validation essentially involves finding data in the library and plotting on the same graph as the predictions. You should also compute the average deviations to provide a numerical measure of the goodness of fit.

Comprehension Questions:
1. Does the SCVP+ model predict higher or lower pure component fugacities than SCVP?
2. Why is it unusual for the deviations from Henry's Law to be positive?
3. Find experimental data for supercritical CO2+acetone. Identify the optimal value of A12 in the SCVP+M1 model to fit these data and compute the root mean square deviation (rmsd) of pressure: rmsd = sqrt(sum(Pcalc-Pexpt)^2).
4. Repeat 3 for N2+acetone. Compare the SCVP, SCVP+, and SCVP+MAB predictions as well as including experimental data.
09.07 - Calculation of Fugacity (Gases) Click here. 40 3

We occasionally require the fugacity in the vapor phase by an EOS other than the PR EOS. (learncheme, 3min) This becomes especially common in Unit 3 when we extend our methods to mixtures. Another skill demonstrated in this screencast is a sample derivation using the pressure dependent formulas. Note that there is a typo in the initial problem statement. The equation of state should be: PV = (1-0.05 P)RT.

Comprehension Questions:

1. Rearrange the given EOS to solve for Z and apply Eq. 9.23 to solve for the change in fugacity. Compare your answer to that given in the screencast. Which method seems easier to you?
2. Use Eq. 7.5 with Eq. 9.23 to derive an expression for the fugacity.
3. Apply the result of #2 to evaluate the fugacity of n-pentane at 398 K and 1 MPa.
4. Does this condition for pentane satisfy Eq. 7.10? Explain.
01.5 Real Fluids and Tabulated Properties Click here. 40 1

Steam quality given temperature and volume (LearnChemE.com, 9min) Steam quality is the fraction of H2O that exists as vapor. Its computation can be accomplished by knowing one of the saturation properties (T or P) and one of the tabulated properties (V,U,H,S). This kind of calculation is sometimes known as the "lever rule" or "inverse lever rule" because the given property acts like the fulcrum on a lever, specifying whether the liquid or vapor property receives the heavier weight. e.g. if the given property is closer to the saturated vapor value, then the vapor value receives a hevierer weight.


Comprehension Questions:
1. Compute the enthalpy (kJ/kg) at 100 C and a quality (q) of  33%.
2. Compute the entropy (kJ/kg-C) at 200 C and a quality of 90%.
09.11 - Stable Roots and Saturation Conditions Click here. 40 1

Selecting Stable Roots (5:41) (msu.edu)

Understanding the relation between stable roots and the vapor pressure is a confusing aspect of working with cubic equations of state. When solving problems with enthalpy or entropy matching, it is important to remember to check for stability of the roots. See also the screencast for section 7.6.
06.2 Derivative Relations Click here. 40 4

Heat Capacity Volume Dependence (uakron.edu, 10min) This example derives how the heat capacity of the gas depends on volume, ie. (∂Cv/∂V)T. It may seem paradoxical that a quantity defined at constant volume can change with respect to volume. The discussion here shows how to solve this puzzle. The sample derivation presented here follows an alternative approach to what is illustrated in Example 6.9 of the textbook.

Comprehension Questions:

1. The van der Waals (vdW) equation of state (EOS) is: P = RT/(V-b) - a/V2.  Evaluate (∂Cv/∂V)T for the vdW EOS.
2. The Soave-Redlich-Kwong (SRK) EOS is: P = RT/(V-b) - a/[V(V+b)]
where a=[1+K*(1-sqrt(T/Tc))]2.  Evaluate (∂Cv/∂V)T for the SRK EOS.
3. Comment on the differences between the results for 1 and 2 above. Do these results change the way you look at the vdW EOS?
03.6 - Energy Balance for Reacting Systems Click here. 40 1

Heat Removal from a Chemical Reactor (LearnChemE.com, 8min) determines heat removal so that a chemical reactor is isothermal following the pathway of Figure 3.5a. The reaction is N2 + 3H2 = 2NH3 at 350C and 1 bar. The pathway to go from products to reactants is to cool the products to 25C (the reference temperature), then "unreact" them back to their initial feed state (reactants), then to heat the reactants back to the inlet condition of the reactor (350C,1bar). Summing up the enthalpy changes over these three steps gives the overall change in enthalpy at the reactor conditions.

Comprehension Questions:
1. Suppose the reaction had been carried out at 2 bars. How would we compute the enthalpy change then?
2. Use this approach to compute the heat of reaction for 2 CH3OH = CH3OCH3 + H2O at 250C and 1 bar.
3. Methanol, dimethyl ether, and water are all liquids at 25C and 1 bar. Did you account for the heat of vaporization when answering Question #2 above? Explain.
09.01 - Criteria for Phase Equilibrium Click here. 40 4

Phase equilibrium in a pure fluid (uakron, 11min) can be contemplated in terms of the following question: Suppose propane exists at a set temperature in an uninsulated piston/cylinder with half the volume as vapor and half as liquid. What is the final pressure when the piston is pressed down. A proper thermodynamic answer leads to the consideration of the Gibbs energy, with implications that open up an entire new world of problems to be solved related to equilibrium partitioning for pure fluids and mixtures.

Comprehension Questions:

1. Write dG for the total piston/cylinder system in terms of the individual phases.
2. What is the criterion for equilibrium in a pure fluid?
3. What is the stable state (L,V,L=V) when GL > GV ?
4. For the vdW fluid at 62C, 0.35 MPa, the following roots were obtained: ZL = 0.02598,
ZV = 0.92718, A=0.08608, B=0.01820. What is the stable state (L,V,L=V)?
5. For the vdW fluid at 62C, 0.25 MPa, the following roots were obtained: ZL = 0.01859,
ZV = 0.94910, A=0.061487, B=0.013000. What is the stable state (L,V,L=V)?

Hint: (G-Gig)/RT = -ln(Z-B)-A/Z + Z - 1 - ln(Z) where A=a*P/(R2T2); B=bP/RT; b=0.125*RTc/Pc
11.12 - Lewis-Randall Rule and Henry's Law Click here. 36 5

Characterizing gas solubility beyond Henry's Law concentrations (uakron.edu, 6min) This presentation shows how to use the M2 model to fit the gas solubility when the pressure deviates from the linear behavior indicated by Henry's Law. It is very similar to the procedure illustrated in Section 11.9, but we use a slightly customized format here.

Comprehension questions:

1. Find experimental data for supercritical CO2+acetone. Identify the optimal value of A12 and A21 in the SCVP+M2 model to fit these data and compute the root mean square deviation (rmsd) of pressure: rmsd = sqrt(sum(Pcalc-Pexpt)^2/NPTS). Also tabulate the %AAD for this system.
2. Repeat 1 for ethylene+water at 100F. (Hint: cf. DECHEMA for reference to Anthony and McKetta, 1967)
08.01 - The Departure Function Pathway Click here. 35 4

Demystifying The Departure Function (11min) (uakron.edu)
...a peek inside the magician's hat. The connection from the real fluid to the ideal gas is not really magic. You can look at it as transforming the interaction potential (ie. u(r)) from 0 (ideal gas) to a Lennard-Jones model (real fluid). Alternatively, you can view it as the difference between the real fluid and ideal gas at each density, summed from zero density (where both exhibit ideal gas behavior) to the density of interest. This latter approach is most convenient and makes good use of our new expertise in derivative manipulations and equations of state.

Comprehension Questions:

1. In the diagram of (A-Ac)/RTc, which state represents the closest point to an ideal gas: A, B, C, or D?
2. Write out the departure function pathway in its various steps to compute "U" = (U-URef).
3. Identify the steps in #2 above as departure function or ideal gas contributions.
4. For propane at 355K and 3MPa, (U-Uig)= -2572 J/mol. We can compute Uig(355K)-Uig(230K)=8000 J/mol. The departure function for liquid propane at 230K, 0.1MPa is (U-Uig)= -16970 J/mol. Compute the value of "U" at 355K and 3MPa relative to liquid propane at 230, and 0.1MPa using this information.
5. Compare your answer to the value given by PREOS.xlsx.
6. Compare your answer to the value given by the pathway of Figure 2.6c. (Hint: use Eqn. 2.47 to decide whether 355K,3MPa corresponds to a vapor or liquid.)

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